scholarly journals Dynamic linear response of a shock/turbulent-boundary-layer interaction using constrained perturbations

2018 ◽  
Vol 840 ◽  
pp. 291-341 ◽  
Author(s):  
Michael C. Adler ◽  
Datta V. Gaitonde
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Linear Response ◽  
Separation Bubble ◽  
Low Frequency ◽  
Linear Dynamics ◽  
Local Linear ◽  
Flow Features ◽  
Shock Position ◽  
Shock Motion

Comprehensive experimental and computational investigations have revealed possible mechanisms underlying low-frequency unsteadiness observed in spanwise homogeneous shock-wave/turbulent-boundary-layer interactions (STBLI). In the present work, we extend this understanding by examining the dynamic linear response of a moderately separated Mach 2.3 STBLI to small perturbations. The statistically stationary linear response is analysed to identify potential time-local and time-mean linear tendencies present in the unsteady base flow: these provide insight into the selective amplification properties of the flow at various points in the limit cycle, as well as asymmetry and restoring mechanisms in the dynamics of the separation bubble. The numerical technique uses the synchronized large-eddy simulation method, previously developed for free shear flows, significantly extended to include a linear constraint necessary for wall-bounded flows. The results demonstrate that the STBLI fosters a global absolute linear instability corresponding to a time-mean linear tendency for upstream shock motion. The absolute instability is maintained through constructive feedback of perturbations through the recirculation: it is self-sustaining and insensitive to external forcing. The dynamics are characterized for key frequency bands corresponding to high–mid-frequency Kelvin–Helmholtz shedding along the separated shear layer $(St_{L}\sim 0.5)$, low–mid-frequency oscillations of the separation bubble $(St_{L}\sim 0.1)$ and low-frequency large-scale bubble breathing and shock motion $(St_{L}\sim 0.03)$, where the Strouhal number is based on the nominal length of the separation bubble, $L$: $St_{L}=fL/U_{\infty }$. A band-pass filtering decomposition isolates the dynamic flow features and linear responses associated with these mechanisms. For example, in the low-frequency band, extreme shock displacements are shown to correlate with time-local linear tendencies toward more moderate displacements, indicating a restoring mechanism in the linear dynamics. However, a disparity between the linearly stable shock position and the mean shock position leads to an observed asymmetry in the low-frequency shock motion cycle, in which upstream motion occurs more rapidly than downstream motion. This is explained through competing linear and nonlinear (mass depletion through shedding) mechanisms and discussed in the context of an oscillator model. The analysis successfully illustrates how time-local linear dynamics sustain several key unsteady broadband flow features in a causal manner.

Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

2017 ◽  
Vol 823 ◽  
pp. 617-657 ◽  
Author(s):  
Vito Pasquariello ◽  
Stefan Hickel ◽  
Nikolaus A. Adams
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
High Reynolds Number ◽  
Separation Bubble ◽  
Low Frequency ◽  
Boundary Layer Interaction ◽  
High Reynolds ◽  
Unsteady Effects

We analyse the low-frequency dynamics of a high Reynolds number impinging shock-wave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by $19.6^{\circ }$. The Reynolds number based on the incoming boundary-layer thickness of $Re_{\unicode[STIX]{x1D6FF}_{0}}\approx 203\times 10^{3}$ is considerably higher than in previous LES studies. The very long integration time of $3805\unicode[STIX]{x1D6FF}_{0}/U_{0}$ allows for an accurate analysis of low-frequency unsteady effects. Experimental wall-pressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise vortices originating in the proximity of the bubble apex. Contrary to previous numerical results on compression ramp configurations, these Görtler-like vortices are not fixed at a specific spanwise position, but rather undergo a slow motion coupled to the separation-bubble dynamics. Consistent with experimental data, power spectral densities (PSD) of wall-pressure probes exhibit a broadband and very energetic low-frequency component associated with the separation-shock unsteadiness. Sparsity-promoting dynamic mode decompositions (SPDMD) for both spanwise-averaged data and wall-plane snapshots yield a classical and well-known low-frequency breathing mode of the separation bubble, as well as a medium-frequency shedding mode responsible for reflected and reattachment shock corrugation. SPDMD of the two-dimensional skin-friction coefficient further identifies streamwise streaks at low frequencies that cause large-scale flapping of the reattachment line. The PSD and SPDMD results of our impinging SWBLI support the theory that an intrinsic mechanism of the interaction zone is responsible for the low-frequency unsteadiness, in which Görtler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.

scholarly journals Large Eddy Simulation of Microvortex Generators in a Turbulent Boundary Layer

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
Andrew P. Heffron ◽  
John J. Williams ◽  
Eldad J. Avital
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Eddy Simulation ◽  
Separation Bubble ◽  
Vortex Formation ◽  
Leading Edge ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Flow Features ◽  
Challenging Environment

Abstract This study investigates the flow physics on microvortex generators (MVGs) in order to improve their performance in turbulent boundary layers (TBLs). TBLs can be a challenging environment for MVGs because of the streamwise length of the generated vortex and the increased parasitic drag of the MVGs. Large eddy simulation (LES) is used to properly resolve the turbulent boundary layer of a flat-plate with a zero-pressure gradient and MVG vane. Three different vane-types are investigated (e423-Mod, triangular, and rectangular vanes) and are studied in a single vane configuration. Important flow features such as a separation bubble on the leading edge of the rectangular vanes which introduced unsteadiness into the vortex formation and degraded the MVG's efficiency was observed. The e423-Mod and triangular vanes were observed to be more aerodynamically efficient. The triangular vane was found to be the most efficient when evaluated immediately downstream of the vane. However, the vortex from the triangular vane decayed very rapidly due to it being formed very close to the wall which degraded its efficiency further downstream. The e423-Mod vane avoided this problem but its drag was very high relative to the strength of the generated vortex and its vortex experienced a brief period of rapid decay immediately downstream decreasing its efficiency. Further downstream, the vortex of the rectangular vane at 16 deg became the most efficient through a combination of low vane drag and low vortex decay in the TBL, demonstrating the need to consider a range of issues when designing an MVG.

scholarly journals Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction

2012 ◽  
Vol 700 ◽  
pp. 16-28 ◽  
Author(s):  
Muzio Grilli ◽  
Peter J. Schmid ◽  
Stefan Hickel ◽  
Nikolaus A. Adams
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Separation Bubble ◽  
Low Frequency ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Layer Interaction ◽  
Mode Decomposition ◽  
Boundary Layer Interaction ◽  
Low Frequency Motion

AbstractThe unsteady behaviour in shockwave turbulent boundary layer interaction is investigated by analysing results from a large eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp. The interaction leads to a very-low-frequency motion near the foot of the shock, with a characteristic frequency that is three orders of magnitude lower than the typical frequency of the incoming boundary layer. Wall pressure data are first analysed by means of Fourier analysis, highlighting the low-frequency phenomenon in the interaction region. Furthermore, the flow dynamics are analysed by a dynamic mode decomposition which shows the presence of a low-frequency mode associated with the pulsation of the separation bubble and accompanied by a forward–backward motion of the shock.

Low-frequency unsteadiness in shock wave–turbulent boundary layer interaction

2012 ◽  
Vol 699 ◽  
pp. 1-49 ◽  
Author(s):  
Stephan Priebe ◽  
M. Pino Martín
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Low Frequency ◽  
Separated Flow ◽  
Frequency Mode ◽  
Statistical Relation ◽  
Boundary Layer Interaction ◽  
Shock Motion ◽  
Low Frequency Mode

AbstractThe low-frequency unsteadiness is characterized in the direct numerical simulation of a shock wave–turbulent boundary layer interaction generated by a $2{4}^{\ensuremath{\circ} } $ compression ramp in Mach 2.9 flow. Consistent with experimental observations, the shock wave in the simulation undergoes a broadband streamwise oscillation at frequencies approximately two orders of magnitude lower than the characteristic frequency of the energetic turbulent scales in the incoming boundary layer. The statistical relation between the low-frequency shock motion and the upstream and downstream flow is investigated. The shock motion is found to be related to a breathing of the separation bubble and an associated flapping of the separated shear layer. A much weaker statistical relation is found with the incoming boundary layer. In order to further characterize the low-frequency mode in the downstream separated flow, the temporal evolution of the low-pass filtered flow field is investigated. The nature of the velocity and vorticity profiles in the initial part of the interaction is found to change considerably depending on the phase of the low-frequency motion. It is conjectured that these changes are due to an inherent instability in the downstream separated flow, and that this instability is the physical origin of the low-frequency unsteadiness. The low-frequency mode observed here is, in certain aspects, reminiscent of an unstable global mode obtained by linear stability analysis of the mean flow in a reflected shock interaction (Touber & Sandham, Theor. Comput. Fluid Dyn., vol. 23, 2009, pp. 79–107).

Dynamics of separation bubble dilation and collapse in shock wave/turbulent boundary layer interactions

Shock Waves ◽  
2019 ◽  
Vol 30 (1) ◽  
pp. 63-75
Author(s):  
M. Waindim ◽  
L. Agostini ◽  
L. Larchêveque ◽  
M. Adler ◽  
D. V. Gaitonde
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Separation Bubble

Growth and breakdown of low-speed streaks leading to wall turbulence

2007 ◽  
Vol 586 ◽  
pp. 371-396 ◽  
Author(s):  
MASAHITO ASAI ◽  
YASUFUMI KONISHI ◽  
YUKI OIZUMI ◽  
MICHIO NISHIOKA
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Low Frequency ◽  
Wall Turbulence ◽  
Linear Stability Theory ◽  
Transition Flow ◽  
Wall Suction ◽  
Low Speed ◽  
Low Speed Streaks ◽  
Near Wall

Two-dimensional local wall suction is applied to a fully developed turbulent boundary layer such that near-wall turbulence structures are completely sucked out, but most of the turbulent vortices in the original outer layer can survive the suction and cause the resulting laminar flow to undergo re-transition. This enables us to observe and clarify the whole process by which the suction-surviving strong vortical motions give rise to near-wall low-speed streaks and eventually generate wall turbulence. Hot-wire and particle image velocimetry (PIV) measurements show that low-frequency velocity fluctuations, which are markedly suppressed near the wall by the local wall suction, soon start to grow downstream of the suction. The growth of low-frequency fluctuations is algebraic. This characterizes the streak growth caused by the suction-surviving turbulent vortices. The low-speed streaks obtain almost the same spanwise spacing as that of the original turbulent boundary layer without the suction even in the initial stage of the streak development. This indicates that the suction-surviving turbulent vortices are efficient in exciting the necessary ingredients for the wall turbulence, namely, low-speed streaks of the correct scale. After attaining near-saturation, the low-speed streaks soon undergo sinuous instability to lead to re-transition. Flow visualization shows that the streak instability and its subsequent breakdown occur at random in space and time in spite of the spanwise arrangement of streaks being almost periodic. Even under the high-intensity turbulence conditions, the sinuous instability amplifies disturbances of almost the same wavelength as predicted from the linear stability theory, though the actual growth is in the form of a wave packet with not more than two waves. It should be emphasized that the mean velocity develops the log-law profile as the streak breakdown proceeds. The transient growth and eventual breakdown of low-speed streaks are also discussed in connection with the critical condition for the wall-turbulence generation.

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